77.1.8 problem 19 (page 30)

Internal problem ID [17827]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 19 (page 30)
Date solved : Monday, March 31, 2025 at 04:34:37 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 11

ode:=diff(y(x),x) = y(x)/x*(1+ln(y(x))-ln(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \,{\mathrm e}^{-c_1 x} \]

✓ Mathematica. Time used: 0.196 (sec). Leaf size: 20

ode=D[y[x],x]==y[x]/x*(1+Log[y[x]]-Log[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x e^{e^{c_1} x} \\ y(x)\to x \\ \end{align*}

✓ Sympy. Time used: 0.581 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-log(x) + log(y(x)) + 1)*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x e^{C_{1} x} \]